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Wednesday, January 10, 2018

Wednesday, January 10, 2018 — 10:30 to 10:30 AM EST

Sparse Estimation for Functional Semiparametric Additive Models

In the context of functional data analysis, functional linear regression serves as a fundamental tool to handle the relationship between a scalar response and a functional covariate. With the aid of  Karhunen–Loève expansion of a stochastic process, a functional linear model can be written as an infinite linear combination of functional principal component scores. A reduced form is fitted in practice for dimension reduction; it is essentially converted to a multiple linear regression model.

Though the functional linear model is easy to implement and interpret in applications, it may suffer from an inadequate fit due to this specific linear representation. Additionally, effects of scalar predictors which may be predictive of the scalar response are neglected in the functional linear model.

Prediction accuracy can be enhanced greatly by incorporating effects of these scalar predictors.

In this talk, we propose a functional semiparametric additive model, which models the effect of a functional covariate nonparametrically and models several scalar covariates in a linear form. We develop the method for estimating the functional semiparametric additive model by smoothing and selecting non-vanishing components for the functional covariate. We show that the estimation method can consistently estimate both nonparametric and parametric parts in the model. Numerical studies will be presented to demonstrate the advantage of the proposed model in prediction.

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